Radiographic imaging such as x-ray imaging has been used for years in medical applications and for non-destructive testing.
Generally, an x-ray imaging system includes an x-ray source and an x-ray detector array consisting of multiple detectors comprising one or many detector elements, i.e. independent means of measuring x-ray intensity/fluence. The x-ray source emits x-rays, which pass through a subject or object to be imaged and are then registered by the detector array. Since some materials absorb a larger fraction of the x-rays than 25 others, an image is formed of the subject or object.
X-ray detectors with photon counting and energy resolving capabilities are becoming common for medical x-ray applications. Generally, a photon counting x-ray detector determines the energy of a photon by comparing the height of the electric pulse 30 generated by a photon interaction in the detector material to a set of comparator voltages. These comparator voltages are also referred to as energy thresholds. Generally, the analog voltage in a comparator is set by a digital-to-analog converter, DAC. The DAC converts a digital setting sent by a controller to an analog voltage with respect to which the heights of the photon pulses can be compared. In order to determine the energy of the photon, it is necessary to know the translation between the digital settings sent to the DAC and the photon energy. This relationship can be expressed as: E=g×DS+m, where E is the energy of the photon, DS is the digital setting, g is referred to as the gain and m is referred to as the offset.
Determining the gain and the offset of the energy thresholds on a photon-counting detector is essential for avoiding artifacts in the reconstructed image. The avoided artifacts include ring artifacts, which arise when channels count a different number of x-rays even though the input x-ray spectrum is identical, due to the different positions of the energy thresholds. Ring artifacts can be mitigated by estimating the gain and the offset for each threshold on all channels and position the energy thresholds on the same position in keV. If the thresholds are on equal position in keV then identical input gives identical output for the different channels.
Also, un-calibrated energy thresholds can introduce a bias in when performing material basis decomposition, making it difficult to perform quantitative material decomposition, i.e. estimating the amount of a certain material in a certain pixel in the reconstructed image.
Further, the position of the lowest threshold, in keV, has a large impact on the overall detection efficiency of the detector. The detected spectrum has large content for low keV and placing the lowest threshold lower implies that more photons can be counted. However, each channel has electronic noise and placing a threshold too low can result in that a channel counts a lot of noise counts. Counting noise 25 degrades the signal and if too much noise is included, the signal cannot be used. Therefore, there is a trade-off in the position of the lowest threshold between including noise and including more real photons and by obtaining accurate values of the gain and the offset one can position the lowest threshold at the optimal position, which can increase the detection efficiency by several percent.
There are several known ways to estimate the gain and offset of a converter acting to create thresholds to a comparator. The most common is to use a mono-energetic x-ray source or a synchrotron x-ray beam and perform a scan of the digital setting to locate the position of the peak in the detected x-ray spectrum, see Refs. [1], [2], [3]. Other methods include performing a scan of the digital setting and identifying a feature in the detected spectrum, see Refs. [4] [5], fitting a model to the detected data [6] or varying the kilovoltage peak, kVp, of an x-ray tube and identifying the highest digital setting value for which counts are registered [7]. Common for all methods in the previous art is that they aim to calibrate all converters on a channel individually.
Even though several methods have been proposed to improve the estimation of the gain and offset of a converter there remains a need within the field to provide mechanisms that further improve the estimation of the gain and offset of a converter in order to obtain an efficient and reliable image reconstruction during e.g. x-ray imaging.